Journal of Physics Condensed Matter

Collective excitations in two-component ultracold quantum matter

Avinaba Mukherjee, Subhendu Saha, Raka Dasgupta

Published May 22, 2025• 2 citations

Abstract

In this paper, we have reviewed a range of theoretical works on collective oscillations in two-component ultracold quantum gases. It is shown that in two-component systems, two key collective modes are generated: a density mode and a spin mode. Using different prototypes of cold bosonic systems as examples, it is shown how these modes at certain parameter values can get converted into Goldstone modes: indicating criticality. Additionally, emergence of roton modes (and roton softening, too) is discussed in the context of two component boson-boson and boson-fermion mixtures, with a particular focus on striped phases. In the fermionic front, it is demonstrated that two-species systems lead to population-imbalanced exotic phases like FFLO and breached pair; and the collective excitations carry very important information about those structures: like the amount of imbalance present, exact pairing structure, etc. Since it is often difficult to resolve such structures in direct experiments, a study of the collective oscillations can prove to be very useful as indirect probes.

DOI: 10.1088/1361-648x/addc28

Related papers

Collective modes as a probe of imbalanced Fermi gases

Jonathan M. Edge, Nigel R. Cooper

We theoretically investigate the collective modes of imbalanced two-component one-dimensional Fermi gases with attractive interactions. This is done for trapped and untrapped systems both at zero and nonzero temperature, using self-consistent mean-field theory and the random phase approximation. We discuss how the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can be detected and the periodicity of the associated density modulations determined from its collective mode spectrum. We also investigate the accuracy of the single-mode approximation for low-lying collective excitations in a trap by comparing frequencies obtained via sum rules with frequencies obtained from direct collective mode calculations. It is found that, for collective excitations where the atomic clouds of the two spin-species oscillate largely in phase, the single-mode approximation holds well for a large parameter regime. Finally, we investigate the collective mode spectrum obtained by parametric modulation of the coupling constant.

arXiv:0912.5275Physical Review AJun 4, 201015 citations

Searching For FFLO States in Ultracold Polarized Fermi Gases: A Numerical Approach

Lu, Hong

Ultracold atomic gases have emerged as an ideal laboratory system to emulate many-body physics in an unprecedentedly controllable manner. Numerous many-body quantum states and phases have been experimentally explored and characterized using the ultracold atomic gases, offering new insights into many exciting physics ranging from condensed matters to cosmology. In this thesis, we will present a systematic numerical study of a novel experimental system, population imbalanced two-component ultracold Fermi gases. We explore the phase diagram of this system in both 3D and 1D especially focusing on the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which is characterized by a spatially oscillating order parameter. In 3D, we solve for the stationary states of trapped imbalanced Fermi gases in a wide range of parameter space with a home-made parallel eigen-solver for Bogoliubov-de Gennes (BdG) equations. Our results show that there exists a metastable state with a FFLO type oscillating order parameter. In 1D, we simulate the dynamical expansion of the population imbalanced Fermi gases from the trap. A numerically quasi-exact scheme, time-evolving block decimation (TEBD), is introduced for the comparative studies with the solution of the time-dependent BdG equation. Our results predict that the existence of FFLO states will leave conspicuous signatures in the density profiles during the expansion. For further understanding of the interplay between the population imbalance and two-body pairing interaction between two spin components, we also study the spin transport properties through trapped ultracold Fermi gases. The preliminary results will be discussed.

Dec 1, 20120 citations

Introduction to FFLO phases and collective mode in the BEC-BCS crossover

R. Combescot

The main focus of this paper is a discussion of what might happen in a BCS superfluid when there is an imbalance between the two populations of fermionic particles forming Cooper pairs, having in mind the case of ultracold Fermi gases. In the last part the evolution in the BEC-BCS crossover of the collective mode arising in such a superfluid (with balanced atomic populations) is briefly considered.

arXiv:cond-mat/0702399Proceedings of the International School of Physics "Enrico Fermi"Feb 16, 20074 citations

Exotic superfluid states of ultra-cold Fermi gases

Tomi Paananen

This is a study of ultra-cold Fermi gases in different systems. This thesis is focused on exotic superfluid states, for an example on the three component Fermi gas and the FFLO phase in optical lattices. In the two-components case, superfluidity is studied mainly in the case of the spin population imbalanced Fermi gases and the phase diagrams are calculated from the mean-field theory. Different methods to detect different phases in optical lattices are suggested. In the three-component case, we studied also the uniform gas and harmonically trapped system. In this case, the BCS theory is generalized to three-component gases. It is also discussed how to achieve the conditions to get an SU(3)-symmetric Hamiltonian in optical lattices. The thesis is divided in chapters as follows: Chapter 1 is an introduction to the field of cold quantum gases. In chapter 2 optical lattices and their experimental characteristics are discussed. Chapter 3 deals with two-components Fermi gases in optical lattices and the paired states in lattices. In chapter 4 three-component Fermi gases with and without a harmonic trap are explored, and the pairing mechanisms are studied. In this chapter, we also discuss three-component Fermi gases in optical lattices. Chapter 5 devoted to the higher order correlations, and what they can tell about the paired states. Chapter 6 concludes the thesis.

Työväentutkimus VuosikirjaMay 28, 20090 citations

Imbalanced Fermi Gases at Unitarity

K. B. Gubbels, Henk T. C. Stoof, Theoretical Physics +3 more

We consider imbalanced Fermi gases with strong attractive interactions, for which Cooper-pair formation plays an important role. The two-component mix-tures consist either of identical fermionic atoms in two different hyperfine states, or of two different atomic species both occupying only a single hyperfine state. In both cases, the number of atoms for each component is allowed to be differ-ent, which leads to a spin imbalance, or spin polarization. Two different atomic species also lead to a mass imbalance. Imbalanced Fermi gases are relevant to condensed-matter physics, nuclear physics and astroparticle physics. They have been studied intensively in recent years, following their experimental realization in ultracold atomic Fermi gases. The experimental control in such a system allows for a systematic study of the equation of state and the phase diagram as a function of temperature, spin polarization and interaction strength. In this re-view, we discuss the progress in understanding strongly-interacting imbalanced Fermi gases, where a main goal is to describe the results of the highly controlled experiments. We start by discussing Feshbach resonances, after which we treat the imbalanced Fermi gas in mean-field theory to give an introduction to the relevant physics. We encounter several unusual superfluid phases, including phase-separation, gapless Sarma superfluidity, and supersolidity. To obtain a more quantitative description of the experiments, we review also more sophisti-cated techniques, such as diagrammatic methods and the renormalization-group theory. We end the review by discussing two theoretical approaches to treat the inhomogeneous imbalanced Fermi gas, namely the Landau-Ginzburg theory and the Bogoliubov-de Gennes approach. Key words:

Jan 1, 201338 citations

Emergent phenomena in quantum mixtures: from ultra-cold gases to light-matter systems

Matteo Caldara

Quantum mixtures of ultra-cold atoms are exceptional platforms which allow to investigate a huge variety of phenomena owing to the exquisite control of interactions between atoms. We present here a theoretical investigation of some distinctive phenomena emerging in these systems which highlight their quantum nature. Balanced mixtures at sufficiently low temperatures are superfluid and, when set into rotation, they display topological excitations in the form of quantum vortices. In many physical systems, especially in quantum mixtures, the scenario is richer as the vortex core is filled, either deliberately or accidentally, by particles and then stable massive vortices appear. The finite inertial mass has an unmistakable dynamical signature in the trajectory of vortices in two-dimensional superfluids. On the one hand, in bosonic mixtures massive vortices may appear in the immiscible regime where one (majority) component features topological excitations and the other (minority) component localizes at the vortex cores. On the other hand, in Fermi superfluids vortices are intrinsically massive, due to the presence of normal component at the vortex core. Together with dissipative effects, the core mass is expected to affect the collective properties of many-vortex systems, such as providing a stabilization mechanism for usual shear-flow instabilities that have been currently investigated in experiments. In the strongly imbalanced regime, quantum mixtures offer a unique viewpoint on the well-known impurity problem. In particular, the strongly-interacting system made of an impurity atom in a Fermi sea can be described in terms of a Fermi polaron, the prototypical realization of Landau's fundamental concept of quasiparticle. We study the behaviour of the moving Fermi polaron, finding a breakdown of the effective mass description at finite momentum which finds a solid confirmation in a cold-atom experiment. A novel type of quantum liquid may also appear in ultra-cold bosonic mixtures from a competition between interactions. When the mean-field attraction is balanced by a repulsion induced by quantum fluctuations, the system stabilizes into a self-bound configuration, known as quantum droplet. While this physics has been explored in the context of quantum gases, we predict here the existence of a similar droplet phase in a solid-state system with light-matter interactions. We consider a spin mixture of exciton-polaritons, hybrid light-matter quasiparticles formed from the strong coupling between excitons (bound electron-hole pairs) and photons in a semiconductor microcavity. This exotic phase could open an alternative avenue to achieve the long-sought quantum polaritonic regime.

Sep 12, 20250 citations